"Lawful characters tell the truth
, keep their word, respect authority, honor tradition, and judge those who fall short of their duties. Chaotic characters follow their consciences, resent being told what to do, favor new ideas over tradition, and do what they promise if they feel like it. “Law” implies
honor, trustworthiness, obedience to authority
, and reliability. On the downside, lawfulness can include closemindedness, reactionary adherence to tradition, judgmentalness, and a lack of adaptability. Those who consciously promote lawfulness say that only lawful behavior creates a society in which people can depend on each other and make the right decisions in full confidence that others will act as they should."
“Chaos” implies
freedom, adaptability, and flexibility. On the downside, chaos can include recklessness, resentment toward legitimate authority, arbitrary actions, and irresponsibility. Those who promote chaotic behavior say that only unfettered personal freedom allows people to express themselves fully and lets society benefit from the potential that its individuals have within them."
I bolded the portions of each that apply to Batman. 5 for lawful and 3 for chaotic. He's more lawful than chaotic